Overview:
In this assignment, you will provide a quick but defensible answer to a question that is of importance to development economics: how have improved roads shaped urbanization in West Africa? This assignment draws heavily on the methods I teach in the “How to” sections of the module, but also forces you to learn some new skills that I did not cover. This assignment consists of ten questions. The answer to each of these questions is a number.
You will learn:
• New techniques in Stata, such as how to work with spatial data.
• How to independently improve your empirical skills when faced with a new task, without guidance or direction.
• How to do well on the coding test for a JPAL-type interview.
Additional instructions:
Your submission will consist of a single pdf. The first page of the pdf will consist of your student number and your numerical answers to the questions asked. The remainder of the pdf will be a log (or similar) file demonstrating that you were able to produce these answers yourself in Stata (or a similar program, or a mix of programs).
For this assignment, I have put three datasets on Moodle:
• AfricapolisCoordinates: Some coordinates for West African cities from the website https://africapolis.org.
• AfricapolisPopulations: Some populations for West African cities from the same website.
• roadnetwork: A set of road segment length and endpoint coordinates that I adapted from the replication files for Jedwab, R., & Storeygard, A. (2022). The average and heterogeneous effects of transportation investments: Evidence from Sub-Saharan Africa 1960–2010. Journal of the European Economic Association, 20(1), 1-38.
Begin by opening the data on cities and keeping only the 250 largest cities by population in 1950. A real thesis or paper would use the full set, but some of the steps below would require more computational power than is reasonable for an assignment like this.
Let us pretend that any two cities that are within 500 km of each other are connected by a dirt road. Assume that dirt road is a straight line – even if that straight line goes over the ocean, the Sahara, or any other obstacle. Cities further apart are not connected by dirt roads.
• Question 1: What is the average length (in km) of a dirt road?
Now, assume that travel along a dirt road costs 20 darseks per km. For Questions 2 and 3 below, I want you to consider the least cost path as given by Dijkstra's algorithm.
• Question 2: What is the travel cost (in darseks) from Lagos to Abuja along the dirt road network?
• Question 3: What is the travel cost (in darseks) from Lagos to Dakar along the dirt road network?
Now, open the file “roadnetwork”. Note that “ORIG_FID” identifies a road segment. Begin by discarding any roads that have more than two nodes. In a real thesis or paper, you’d need to manually correct these, but I want to keep things simpler for this assignment.
I made these coordinates in ArcMap. ArcMap can sometimes give very slightly different coordinates to two instances of the same point location. This displacement would lead us to mistakenly think that two segments aren’t connected when they really are. So, round all latitude and longitude coordinates to the nearest 0.01 degrees. If any two points have the same rounded coordinates, treat them as the same node in this network.
• Question 4: How many unique nodes are in the network?
Connect every city to the nearest node in this network using a straight line dirt road, as long as the nearest node in the network is within 100 km. In a real thesis or paper, you’d find the nearest point on a node or edge, but I want to keep things simpler for this assignment.
• Question 5: How long (in km) is the average dirt road from a city to its closest node in the road network?
In addition to assuming that a dirt road costs 20 darseks per km to travel, assume that the cost in darseks per km is:
• 10 for road type 0
• 2 for road type 1
• 2 for road type 2
• 3 for road type 3
• 10 for road type 5
• 1.5 for road type 8
• 10 for road type 9
For the questions below, I want you to consider the least cost paths as given by Dijkstra's algorithm along a road network that combines a) the dirt roads that connect cities, b) the dirt roads that connect cities to the segments in the file “roadnetwork”, and c) the segments in the file “roadnetwork”.
• Question 6: What is the travel cost (in darseks) from Lagos to Dakar along the 1970 road network?
Now, I want you to compute “market access” for each city in the data, in each year, as given by the formula:
ππππππ‘π΄ππππ π π = ∑ πππ−π ππ
π≠π
That is, the Market Access of city i is a sum over all other cities j in the network of that other city’s population ππ, deflated by πππ, the travel cost from i to j. This deflation occurs with an elasticity of π = 8.22.
• Question 7: What is Lagos' market access using the 1970 road network and city populations as of 1950?
While the use of 1950 populations is anachronistic and will understate market access, this is standard in the literature since use of predetermined populations means that the measure of market access only changes over time due to changes in the transportation network.
In a regression that includes the years 1970, 1980, 1990, 2000, and 2010, regress the log of city population on the log of market access based on the road network for each year but using the populations from 1960 to compute market access. Include in this regression fixed effects for city and for year. Cluster standard errors by city.
• Question 8: What is the standard error on log market access in this regression?
An alternative, cross-sectional approach, might construct an instrument for market access using what Redding and Turner call an “inconsequential places” approach, exploiting the fact some cities are close to the transportation network simply because they are on a path between two other cities that would have otherwise been connected.
Take the 25 largest cities by population in 1950. Using Prim’s algorithm, construct a minimum spanning tree that connects them with straight lines and that minimizes the total length of the tree.
Now, consider the full set of 250 cities.
• Question 9: How far is the average city from this minimum spanning tree (in km)?
Using the command “acreg” in Stata, run a regression where the dependent variable is the log of city population in 1970. The independent variable is the log of market access in 1970,
computed using the 1970 road network and 1970 city populations. Instrument for this with distance from the spanning tree. Exclude the 25 cities used to construct the tree. Adjust the standard errors for spatial dependence up to a cutoff of 250 km.
• Question 10: What is the standard error on log market access in this regression?
In a real thesis or paper, you would need to add several other modes of transport to this network (e.g. oceans, rivers) and you would need to consider access to markets outside West Africa.
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